The answer is yes; we believe in the Trinity of the Bible; but not the Trinity of post-Apostate Christendom. The English word Trinity is derived from Latin Trinitas, meaning “the number three, a triad”. The corresponding word in Greek is Τριάς, meaning “a set of three” or “the number three”. (See Wikipedia article on the Trinity.)
It simply referred to the three members of the Godhead—the Father, Son, and the Holy Ghost. It did not have the connotations that modern Trinitarians like to put on it. Other English equivalents of the word could be trio, triad, trilogy, triple, triumvirate, or trine. They all basically convey the same idea. They mean three! Its use in early Christianity came out of the realization that the three members of the Godhead are sometimes referenced or invoked together or as though acting in concert, as in these quotes:
Matthew 3:16–17: “And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.” (See also Mark 1:10–11; Luke 3:22; John 1:32.)
Luke 1:35: “And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.”
Hebrews 9:14: “How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?”
Acts 7:55: “But he, being full of the Holy Ghost, looked up stedfastly into heaven, and saw the glory of God, and Jesus standing on the right hand of God,”
Matthew 28:19: “Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:”
2 Corinthians 13:14: “The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Ghost, be with you all. Amen.”
That is how the word Trinity originated. It simply meant the three members of the Godhead. It was not an attempt to define how the three are united, act in unison, or are “one”. Well, Latter-day Saints very much believe in the three members of the Godhead—the Father, Son, and the Holy Ghost. Our very first Article of Faith states that “We believe in God the Eternal Father, and in His Son Jesus Christ, and in the Holy Ghost”. That is the Trinity.
Latter-day Saints who discuss this subject with Christians of other faiths, or with LDS critics, are often unwilling to say that we believe in the Trinity, because they associate the word with the Trinitarian theology of traditional Christianity. But that is a mistake. When the critics of the Church assert that Mormons don’t believe in the Trinity, they want to create the false impression that Mormons do not believe in the three members of the Godhead—the Father, Son, and the Holy Ghost—which of course is not correct. Mormons very much believe in the three members of the Godhead. So the correct answer to that question is that Mormons believe in Trinity of the Bible, which is the correct doctrine of the Trinity; but not in Trinitarianism, or in the Trinitarian theology of traditional Christianity. They are two different things. Trinitarianism has no biblical basis. It is a false theology that developed after the Apostasy of the early Christian church.